Find the polynomial having roots at $0$ , $- 1$ , $1$ , $- 4$ and $4$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{5} - 17 x^{3} + 16 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$0$	$x$
$- 1$	$x + 1$
$1$	$x - 1$
$- 4$	$x + 4$
$4$	$x - 4$

Step 2: Multiply the factors together:

P (x) = x \cdot (x + 1) \cdot (x - 1) \cdot (x + 4) \cdot (x - 4) = x^{5} - 17 x^{3} + 16 x

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Find the polynomial having roots at 0 , −1 , 1 , −4 and 4 .

The polynomial generated from the given zeros is: P(x)=x5−17x3+16x

Find the polynomial having roots at $0$ , $- 1$ , $1$ , $- 4$ and $4$ .

The polynomial generated from the given zeros is: $P (x) = x^{5} - 17 x^{3} + 16 x$